Find a polar equation for the curve represented by the given cartesian equation x + y = 1

Solution:

Given, the cartesian equation is x + y = 1

Converting to polar coordinates,

x = rcosθ

y = rsinθ

Now, x + y = 1 becomes

rcosθ + rsinθ = 1

r(cosθ + sinθ) = 1

Therefore, the polar equation for the curve is r(cosθ + sinθ) = 1.

Example:

Find a polar equation for the curve represented by the given cartesian equation 3x + y = 5

Solution:

Given, the cartesian equation is x + y = 5

Converting to polar coordinates,

x = rcosθ

y = rsinθ

Now, 3x + y = 5 becomes

3rcosθ + rsinθ = 5

r(3cosθ + sinθ) = 5

Therefore, the polar equation for the curve is r(3cosθ + sinθ) = 5.

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Find a polar equation for the curve represented by the given cartesian equation x + y = 1

Summary:

A polar equation for the curve represented by the given cartesian equation x + y = 1 is r(cosθ+sinθ) = 1.